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Optimal nonparametric multivariate change point detection and localization
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Padilla, Oscar Hernan Madrid, Yu, Yi, Wang, Daren and Rinaldo, Alessandro (2022) Optimal nonparametric multivariate change point detection and localization. IEEE Transactions on Information Theory, 68 (3). pp. 1922-1944. doi:10.1109/TIT.2021.3130330 ISSN 0018-9448.
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WRAP-Optimal-nonparametric-multivariate-change-point-detection-localization-2021.pdf - Accepted Version - Requires a PDF viewer. Download (915Kb) | Preview |
Official URL: http://dx.doi.org/10.1109/TIT.2021.3130330
Abstract
We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent p-dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown times, called change points. We quantify the size of the distributional change at any change point with the supremum norm of the difference between the corresponding densities. We are concerned with the localization task of estimating the positions of the change points. In our analysis, we allow for the model parameters to vary with the total number of time points, including the minimal spacing between consecutive change points and the magnitude of the smallest distributional change. We provide information-theoretic lower bounds on both the localization rate and the minimal signal-to-noise ratio required to guarantee consistent localization. We formulate a novel algorithm based on kernel density estimation that nearly achieves the minimax lower bound, save possibly for logarithm factors. We have provided extensive numerical evidence to support our theoretical findings.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Nonparametric statistics, Kernel functions, Ubiquitous computing, Information theory | |||||||||
| Journal or Publication Title: | IEEE Transactions on Information Theory | |||||||||
| Publisher: | IEEE | |||||||||
| ISSN: | 0018-9448 | |||||||||
| Official Date: | March 2022 | |||||||||
| Dates: |
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| Volume: | 68 | |||||||||
| Number: | 3 | |||||||||
| Page Range: | pp. 1922-1944 | |||||||||
| DOI: | 10.1109/TIT.2021.3130330 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 27 January 2022 | |||||||||
| Date of first compliant Open Access: | 27 January 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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